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Intern  Joined: 17 Jan 2012
Posts: 41
GMAT 1: 610 Q43 V31 If Father's age is 1 less than twice the son's age, what is  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 45% (02:49) correct 55% (02:37) wrong based on 375 sessions

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If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son

Originally posted by docabuzar on 31 Jan 2012, 04:50.
Last edited by docabuzar on 31 Jan 2012, 13:24, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58443
Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"

Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: S=25 and N=13 or S=27 and N=14 .

Hope it's clear.
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Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"

Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: S=25 and N=13 or S=27 and N=14 .

Hope it's clear.

Bunnel: will the equation here not be F-1 =2S ( Father's age is 1 less than twice the son's age)
Intern  Joined: 17 Jan 2012
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GMAT 1: 610 Q43 V31 Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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Its all in the wording. Father is 1 less than twice of son, so in other words twice of son is 1 more than father

F = 2S -1

Had it been like " Father is 1 more than twice the son " then F=2S+1 or F-1=2S.

Hope I have added some thing.
Manager  Status: MBA Aspirant
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Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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docabuzar wrote:
Its all in the wording. Father is 1 less than twice of son, so in other words twice of son is 1 more than father

F = 2S -1

Had it been like " Father is 1 more than twice the son " then F=2S+1 or F-1=2S.

Hope I have added some thing.

Hey thanks for the explanation. I just messed up with the words.
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Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"

Gimme Kudos if you like the question

Look at the big picture. You can solve this question quickly using intuition.

Father's age is almost as much as twice of son's age. (just 1 less)
Son's age = NM, Father's age = MN

Say, son's age is 12 then father's is 21 (3 less than twice)
Say, son's age is 13 then father's is 31 (much more than twice)
I hope you understand that you can give up on the 10s series here because the gap will keep widening (diff b/w 14 and 41 will be even more)

Say, son's age is 24 then father's is 42 (much less than twice)
Say, son's age is 25, then father's is 52 (more than twice so give up on the 20s series too)

Say son's age is 36, then father's is 63 (much less than twice)
Say son's age is 37, then father's is 73 (1 less than twice. Got it!)

It's easy to say that there will be no other such combination because 49, 94 doesn't work. Nothing in 50s, 60s and so on will work because we need to stick to 2 digit numbers.

Hence, only statement 1 is sufficient.
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Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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subhajeet wrote:
Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"

Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: S=25 and N=13 or S=27 and N=14 .

Hope it's clear.

Bunnel: will the equation here not be F-1 =2S ( Father's age is 1 less than twice the son's age)

It's all about word translation: father's age is 1 less than twice the son's age, so F is less than 2S by 1 --> so we need to add 1 to F to get 2S --> F+1=2S.

Hope it's clear
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Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"

Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: S=25 and N=13 or S=27 and N=14 .

Hope it's clear.

Hello can you elaborate if it is possible? how did we come up with F=10M+N and S=10N+M , Basically i understood how u solved it but i cannot comprehend the way we approach it initially

Thank you in advance
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Posts: 58443
Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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stampap wrote:
Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"

Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: S=25 and N=13 or S=27 and N=14 .

Hope it's clear.

Hello can you elaborate if it is possible? how did we come up with F=10M+N and S=10N+M , Basically i understood how u solved it but i cannot comprehend the way we approach it initially

Thank you in advance

This is a way of writing a two-digit number. Any two-digit integer can be represented as 10a+b (where a and b are single digit integers), for example 37=3*10+7, 88=8*10+8, etc.
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Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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Oh yes! silly me , i had completely forgot it , now its clear!

thank you bunuel
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Re: If Father's age is 1 less than twice the son's age, what is  [#permalink]

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_________________ Re: If Father's age is 1 less than twice the son's age, what is   [#permalink] 03 Mar 2019, 04:41
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